Abstract: Applications of two kinds of capital allocation principles were studied: one was axiomatic allocation which had been known, and the other was generalized weighted allocation. Firstly, several known risk measures were listed. Based on a axiomatic method, allocation formulae with respect to these risk measures were given. Then in view of a specific numerical model, its allocation results were calculated. Secondly, generalized weighted allocation, which was an extension of weighted allocation, was considered. A method for comparing the amounts of generalized weighted capital allocations under two different aggregate losses, which stems from diversifying property, was mainly discussed. And some special examples were given.

Key words: risk measure, directional derivative, conditional expectation, capital allocation, risk measure, directional derivative, conditional expectation